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When using a potentially noisy power supply, how much should you worry about noise above the frequency bands you are interested in?

For example, if I have an instrument amp with a bandwidth of 1kHz, should I be worried about 1MHz noise?

Put another way: is it common for 1MHz noise to downconvert into noise in my frequency band, or is 1MHz noise going to pretty much stay at 1MHz?

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    \$\begingroup\$ 1 kHz and 1 MHz is a bit extreme, but in general I worry most about high frequency noise, because an opamp's PSRR tends to decrease with frequency. \$\endgroup\$ Commented Aug 18, 2016 at 17:10
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    \$\begingroup\$ Just because an amplifier has a gain bandwidth of 1 kHz, is no reason to believe its power supply sensitivity has that bandwidth. Noise can easily rectify or modulate and show up as DC or other frequencies. \$\endgroup\$
    – Whit3rd
    Commented Aug 19, 2016 at 2:29

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Stopping noise at the source is way better than preventing noise from, say, dropping a cell phone call. Also, a 1MHz &, say, a 1.001MHz signal can mix creating an audible 1KHz signal. So do invest in stuff like a cheap ferrite bead to stop high freq noise.

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